Math 655 - Introduction to Topology

Math. 655 is an introduction to the basic concepts of modern topology: metric spaces, topological spaces,
connectedness, compactness, completeness, quotient spaces, manifolds, and classification of surfaces.
While the course will emphasize the geometric aspects of topology, some applications to analysis will
also be discussed, such as the Banach fixed point theorem and the existence of solutions to first order
differential equations. Math. 655 is the first of a year long sequence. The followup courses Math. 656
and 657 will discuss fundamental groups and covering spaces and homology respectively.